17. A pair of jeans costs $60. The sales tax is 8.25%. What is the total cost for the pair of jeans?

Student 1

I rounded 8.25% to 10%, 10% of $60 is 6, so the total cost is $66. But I know the answer is slightly lower because I’d rounded up.

Student 2

I knew 10% would be $6, so the tax is less than that. Then I just ignored the % sign and the 0 in 60, so that the math I did mentally was 825 times 6. I got 4950. Since I knew the answer was less than 6, I knew the number I wanted was $4.95. Add this to $60, that’s $64.95.

Student 3

8% of $60 is $4.80

.25% of $60 is 15 cents

Add above to get $4.95

Student 4

I set up the problem as 2 fractions being multiplied: (60/1) × (8/100) = 480/100 = 4.8. Add 60 to 4.8, that’s $64.8, but since I rounded the 8.25% to 8%, I think the answer is closer to $65.

18. What is 3.75 x 32?

Student 1

32 x 3 = 96

I think of 0.75 as 3/4, and 1/4 of 32 is 8, so 3/8 is 24

96 + 24 = 120

Student 2

I rounded 3.75 to 4, and did 32 x 4 = 128

Since it’s 1/4 less, and 1/4 of 32 is 8, I subtracted 8 from 128 to get 120

Student 3

I changed the problem by multiplying 3.75 by 4 and divide 32 by 4.

3.75 x 4 = 3(4) + 0.75(2) + 0.75(2) = 12 + 1.5 + 1.5 = 15

32 ÷ 4 = 8

15 x 8 = 120

Student 4

3 x 32 = 96

To multiply 0.75 and 32, I kept doubling 0.75 until it’s easy. So, 0.75 doubled is 1.5, and add another pair of 0.75 would give me 3

Since it took 4 sets of 0.75 to make 3, then there are 8 of these sets in 32

3 x 8 = 24

Add this 24 to 96, I get 120

Mrs. Nguyen

I shared this strategy with them as no one had mentioned it.

3/8 = 0.375

So 3.75 is 3/8 of 10

32 x 10 = 320

3/8 of 320 = 120

Another strategy, similar to Student 3’s:

3.75 x 2 = 7.5 and 32 ÷ 2 = 16

7.5 x 2 = 15 and 16 ÷ 2 = 8

15 x 2 = 30 and 8 ÷ 2 = 4

30 x 4 = 120

19. What is 37.5 x 16?

Student 1

37.5 x 10 = 375

37.5 + 37.5 = 75

75 x 3 = 225

375 + 225 = 600

Student 2

37.5 x 2 = 75

16 ÷ 2 = 8

75 x 8 = 600

Student 3

40 x 16 = 640 (I did 4 times 16, then add the 0)

I went over by 2.5, so 2.5 x 16 = 2(16) + 0.5(16) = 32 + 8 = 40

640 – 40 = 600

Student 4

37.5 x 2 = 75

16 ÷ 2 = 8

75 x 2 = 150

8 ÷ 2 = 4

150 x 4 = 600

20. You need to cook a 24-pound turkey. The cookbook says it takes 15 minutes to cook every pound of turkey weight. How long will take to cook the turkey?

I stole this question from David Coffey. Actually, I just asked the kids what 24 x 15 is.

Student 1

I broke the 15 into 3 chunks of 5.

24 x 5 = 120

3 x 120 = 360

Student 2

I changed the problem to make the numbers nicer.

24 ÷ 4 = 6

15 x 4 = 60

6 x 60 = 360

Student 3

I just saw 15 on the clock face as a quarter. It takes 4 of these to make 1 whole. So I did 24 divided by 4 to get 6. Then 6 times 60 (full clock) to get 360.

Student 4

I changed the problem.

24 ÷ 2 = 12

15 x 2 = 30

12 x 30 = 360

Student 5

I broke up 24 into 20 and 4.

20 x 15 = 300

4 x 15 = 60

300 + 60 = 360

Student 6

I broke up the numbers.

24 x 10 = 240

20 x 5 = 100

4 x 5 = 20

240 + 100 + 20 = 360

Student 7

20 x 10 = 200

20 x 5 = 100

4 x 10 = 40

4 x 5 = 20

Add them all up to get 360.

Student 8

I divided both numbers by 3 to get easier numbers.

24 ÷ 3 = 8

15 ÷ 3 = 5

8 x 5 = 40

Because I divided both numbers by 3, I have to multiply the 40 by 3, and then by 3 again. So 40 times 3 is 120, then 120 times 3 is 360.